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What is the greatest prime factor of 2^(10)*5^4 - 2^(13)*5^2 + 2^(14)?

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GeminiHeat
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What is the greatest prime factor of 2^(10)*5^4 - 2^(13)*5^2 + 2^(14)? [#permalink] New post   24 Aug 2021, 05:09
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What is the greatest prime factor of \(2^{10}*5^4 - 2^{13}*5^2 + 2^{14}\)?

(A) 2

(B) 3

(C) 7

(D) 11

(E) 13
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C
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arjunbir
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Re: What is the greatest prime factor of 2^(10)*5^4 - 2^(13)*5^2 + 2^(14)? [#permalink] New post   26 Aug 2021, 13:41
can anyone help me with the solution?
Thank you
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rx10
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Re: What is the greatest prime factor of 2^(10)*5^4 - 2^(13)*5^2 + 2^(14)? [#permalink] New post   26 Aug 2021, 19:22
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\(2^{10}*5^4 - 2^{13}*5^2 + 2^{14}\)

Taking \(2^{10}\) common

\(2^{10} (5^4 - 2^3*5^2 + 2^{4})\)

\(2^{10}(625 - 200 + 16)\)

\(2^{10}(441)\)

\(2^{10}(7 * 7 * 3 * 3)\)

The greatest prime factor \(= 7\)

Answer C


arjunbir wrote:
can anyone help me with the solution?
Thank you
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himanshu13
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Re: What is the greatest prime factor of 2^(10)*5^4 - 2^(13)*5^2 + 2^(14)? [#permalink] New post   26 Aug 2021, 22:28
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rx10 wrote:
\(2^{10}*5^4 - 2^{13}*5^2 + 2^{14}\)

Taking \(2^{10}\) common

\(2^{10} (5^4 - 2^3*5^2 + 2^{4})\)

\(2^{10}(625 - 200 + 16)\)

\(2^{10}(441)\)

\(2^{10}(7 * 7 * 3 * 3)\)

The greatest prime factor \(= 7\)

Answer C


arjunbir wrote:
can anyone help me with the solution?
Thank you



What if we take 5^2 also as common :

2^10 * 5^2 (5^2 - 2^3 + 2^4/5^2)
2^10 * 5^2 (25 - 8 + 16/25)
2^10 * 5^2 (17.64)
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rx10
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Re: What is the greatest prime factor of 2^(10)*5^4 - 2^(13)*5^2 + 2^(14)? [#permalink] New post   26 Aug 2021, 23:39
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And what answer will you choose? We need the greatest possible.

himanshu13 wrote:
What if we take 5^2 also as common :

2^10 * 5^2 (5^2 - 2^3 + 2^4/5^2)
2^10 * 5^2 (25 - 8 + 16/25)
2^10 * 5^2 (17.64)
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himanshu13
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Re: What is the greatest prime factor of 2^(10)*5^4 - 2^(13)*5^2 + 2^(14)? [#permalink] New post   26 Aug 2021, 23:55
rx10 wrote:
And what answer will you choose? We need the greatest possible.

himanshu13 wrote:
What if we take 5^2 also as common :

2^10 * 5^2 (5^2 - 2^3 + 2^4/5^2)
2^10 * 5^2 (25 - 8 + 16/25)
2^10 * 5^2 (17.64)



I cannot find 7 , so I am confused?
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gmatclubot
Re: What is the greatest prime factor of 2^(10)*5^4 - 2^(13)*5^2 + 2^(14)? [#permalink]
26 Aug 2021, 23:55
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